Quantum Resonator Research Articles

External-level assisted cooling by measurement

A quantum resonator in a thermal-equilibrium state with a high temperature has a large average population and is featured with significant occupation over Fock states with a high excitation number. The resonator could be cooled down via continuous measurements on the ground state of a coupled two-level system (qubit). We find, however, that the measurement-induced cooling might become inefficient in the high-temperature regime. Beyond the conventional strategy, we introduce strong driving between the excited state of the qubit and an external level. It can remarkably broaden the cooling range in regard to the non-vanishing populated Fock states of the resonator. Without any precooling procedure, our strategy allows a significant reduction of the populations over Fock states with a high excitation number, giving rise to nondeterministic ground-state cooling after a sequence of measurements. The driving-induced fast transition constrains the resonator and the ancillary qubit at their ground state upon measurement and then simulates the quantum Zeno effect. Our protocol is applied to cool down a high-temperature magnetic resonator. Additionally, it is generalized to a hybrid cooling protocol by interpolating the methods with and without strong driving, which can accelerate the cooling process and increase the overlap between the final state of the resonator and its ground state.

Integrated Whispering-Gallery-Mode Resonator for Solid-State Coherent Quantum Photonics.

Tailored photonics cavities enhance light-matter interactions, ultimately enabling a fully coherent quantum interface. Here, we report an integrated microdisk cavity containing self-assembled quantum dots to coherently route photons between different access waveguides. We measure a Purcell factor of Fexp = 6.9 ± 0.9 for a cavity quality factor of about 10,000, allowing us to observe clear signatures of coherent scattering of photons by the quantum dots. We show how this integrated system can coherently reroute photons between the drop and bus ports and how this routing is controlled by detuning the quantum dot and resonator or through the strength of the excitation beam, where a critical photon number less than one photon per lifetime is required. We discuss the strengths and limitations of this approach, focusing on how the coherent scattering and single-photon nonlinearity can be used to increase the efficiency of quantum devices such as routers or Bell-state analyzers.

Resonant enhancement of grazing incidence neutron scattering for the characterization of thin films

We use signal enhancement in a quantum resonator for the characterization of a thin layer of vanadium hydride using neutron reflectometry and demonstrate that pressure-concentration isotherms and expansion coefficients can be extracted from the measurement of totally externally reflected neutrons only. Moreover, a consistent data analysis of the attenuation cross section allows us to detect and quantify off-specular and small angle scattering. As our experiments are effective direct beam measurements, combined with resonant signal enhancement, counting times become considerably reduced. This allows us to overcome the challenges resulting from the comparatively low brilliance of neutron beams for grazing incidence scattering experiments. Further, we discuss the potential of resonant enhancement to increase any scattering, which is of particular interest for grazing incidence small angle neutron scattering and spectroscopy.

Thermal rectification through a nonlinear quantum resonator

We present a comprehensive and systematic study of thermal rectification in a prototypical low-dimensional quantum system -- a non-linear resonator: we identify necessary conditions to observe thermal rectification and we discuss strategies to maximize it. We focus, in particular, on the case where anharmonicity is very strong and the system reduces to a qubit. In the latter case, we derive general upper bounds on rectification which hold in the weak system-bath coupling regime, and we show how the Lamb shift can be exploited to enhance rectification. We then go beyond the weak-coupling regime by employing different methods: i) including co-tunneling processes, ii) using the non-equilibrium Green's function formalism and iii) using the Feynman-Vernon path integral approach. We find that the strong coupling regime allows us to violate the bounds derived in the weak-coupling regime, providing us with clear signatures of high order coherent processes visible in the thermal rectification. In the general case, where many levels participate to the system dynamics, we compare the heat rectification calculated with the equation of motion method and with a mean-field approximation. We find that the former method predicts, for a small or intermediate anharmonicity, a larger rectification coefficient.

A hybrid (Al)GaAs-LiNbO3 surface acoustic wave resonator for cavity quantum dot optomechanics

A hybrid device comprising a (Al)GaAs quantum dot heterostructure and a LiNbO3 surface acoustic wave resonator is fabricated by heterointegration. High acoustic quality factors Q>4000 are demonstrated for an operation frequency f≈300 MHz. The measured large quality factor-frequency products Q×f>1012 ensure the suppression of decoherence due to thermal noise for temperatures exceeding T>50 K. Frequency and position dependent optomechanical coupling of single quantum dots and resonator modes is observed.

Probabilistic motional averaging

In a continuous measurement scheme a spin-1/2 particle can be measured and simultaneously driven by an external resonant signal. When the driving is weak, it does not prevent the particle wave-function from collapsing and a detector randomly outputs two responses corresponding to the states of the particle. In contrast, when driving is strong, the detector returns a single response corresponding to the mean of the two single-state responses. This situation is similar to a motional averaging, observed in nuclear magnetic resonance spectroscopy. We study such quantum system, being periodically driven and probed, which consists of a qubit coupled to a quantum resonator. It is demonstrated that the transmission through the resonator is defined by the interplay between driving strength, qubit dissipation, and resonator linewidth. We demonstrate that our experimental results are in good agreement with numerical and analytical calculations.

Magnons at low excitations: Observation of incoherent coupling to a bath of two-level systems

Collective magnetic excitation modes, magnons, can be coherently coupled to microwave photons in the single excitation limit. This allows for access to quantum properties of magnons and opens up a range of applications in quantum information processing, with the intrinsic magnon linewidth representing the coherence time of a quantum resonator. Our measurement system consists of a yttrium iron garnet (YIG) sphere and a three-dimensional (3D) microwave cavity at temperatures and excitation powers typical for superconducting quantum circuit experiments. We perform spectroscopic measurements to determine the limiting factor of magnon coherence at these experimental conditions. Using the input-output formalism, we extract the magnon linewidth $\kappa_\mathrm{m}$. We attribute the limitations of the coherence time at lowest temperatures and excitation powers to incoherent losses into a bath of near-resonance two-level systems (TLSs), a generic loss mechanism known from superconducting circuits under these experimental conditions. We find that the TLSs saturate when increasing the excitation power from quantum excitation to multi-photon excitation and their contribution to the linewidth vanishes. At higher temperatures, the TLSs saturate thermally and the magnon linewidth decreases as well.

Nuclear Spin Incoherent Neutron Scattering from Quantum Well Resonators.

We report the detection and quantification of nuclear spin incoherent scattering from hydrogen occupying interstitial sites in a thin film of vanadium. The neutron wave field is enhanced in a quantum resonator with magnetically switchable boundaries. Our results provide a pathway for the study of dynamics at surfaces and in ultrathin films using inelastic and/or quasielastic neutron scattering methods.

Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

We study the spectral properties of Markovian driven-dissipative quantum systems, focusing on the nonlinear quantum van der Pol oscillator as a paradigmatic example. We discuss a generalized Lehmann representation, in which single-particle Green's functions are expressed in terms of the eigenstates and eigenvalues of the Liouvillian. Applying it to the quantum van der Pol oscillator, we find a wealth of phenomena that are not apparent in the steady-state density matrix alone. Unlike the steady state, the photonic spectral function has a strong dependence on interaction strength. Further, we find that the interplay of interaction and non-equilibrium effects can result in a surprising ‘negative density of states’, associated with a negative temperature, even in absence of steady state population inversion.

One-dimensional spin-orbit coupling Bose gases with harmonic trapping

Rabi model is a popular model in quantum optics and describes a two-level system coupling to a quantum resonator. The fruitful physics appears when the coupling strength is comparable to the frequency of the resonator. We investigate the Bose gases of Raman induced spin-orbit coupling with an external harmonic trapping. Using the displacement Fock state in quantum optics we seek for an approximate ground state. We find the superposition state of left and right displaced oscillator state with odd parity has lower energy than the displaced state itself. Besides, we study the time evolution of both the momentum and the position of the system at single particle level to demonstrate the Zitterbewegung oscillating characteristics, which present an intuitive physical picture and are in qualitative agreement with the relevant experimental results. The results are useful to study the Rabi model in deep-strong coupling regime, the model that is difficult to realize in today’s experiment based on the high controllability property of laser, and these results are also instructive for the cold atom physics field.

Ultrastrong-coupling regime of nondipolar light-matter interactions

We present a circuit-QED scheme which allows to reach the ultrastrong coupling regime of a nondipolar interaction between a single qubit and a quantum resonator. We show that the system Hamiltonian is well approximated by a two-photon quantum Rabi model and propose a simple scattering experiment to probe its fundamental properties. In particular, we identify a driving scheme that reveals the change in selection rules characterizing the breakdown of the rotating-wave approximation and the transition from strong to ultrastrong two-photon interactions. Finally, we show that a frequency crowding in a narrow spectral region is observable in the output fluoresce spectrum as the coupling strength approaches the collapse point, paving the way to the direct observation of the onset of the spectral collapse in a solid-state device.

Analog–Digital Quantum Simulation of the Dicke Model with Superconducting Circuits

We propose a concept of mixed analog–digital quantum simulation of the Dicke model with ensembles of superconducting qubits coupled to the single-mode microwave resonators. Using both single-qubit and twoqubit quantum logic gates, it should be possible to engineer different initial conditions for the ensemble of qubits. Since qubits can interact through the photon field of a common quantum resonator, it is attractive to examine the time evolution of this system depending on various characteristics of the initial state, including entanglement and symmetry. We here study theoretically the dynamics of such systems taking into account energy dissipation, pure decoherence as well as disorder in qubits excitation frequencies, which are unavoidable for macroscopic artificial quantum systems. We reveal unusual effects of these imperfections on the dynamics.

A quantum walk in phase space with resonator-assisted double quantum dots**Project supported by the National Natural Science Foundation of China (Grant No. 11474049) and CAST Innovation Fund.

We implement a quantum walk in phase space with a new mechanism based on the superconducting resonator-assisted double quantum dots. By analyzing the hybrid system, we obtain the necessary factors implementing a quantum walk in phase space: the walker, coin, coin flipping and conditional phase shift. The coin flipping is implemented by adding a driving field to the resonator. The interaction between the quantum dots and resonator is used to implement conditional phase shift. Furthermore, we show that with different driving fields the quantum walk in phase space exhibits a ballistic behavior over 25 steps and numerically analyze the factors influencing the spreading of the walker in phase space.

Thermodynamic cycle in a cavity optomechanical system

A cavity optomechanical system is initiated by the radiation pressure of a cavity field onto a mirror element acting as a quantum resonator. This radiation pressure can control the thermodynamic character of the mirror to some extent, such as by cooling its effective temperature. Here, we show that by properly engineering the spectral density of a thermal heat bath that interacts with a quantum system, the evolution of the quantum system can be effectively turned on and off. Inside a cavity optomechanical system, when the heat bath is realized by a multi-mode oscillator modelling of the mirror, this on–off effect translates to infusion or extraction of heat energy in and out of the cavity field, facilitating a four-stroke thermodynamic cycle.

Excitation spectrum as a resource for efficient two-qubit entangling gates

Physical systems representing qubits typically have one or more accessible quantum states in addition to the two states that encode the qubit. We demonstrate that active involvement of such auxiliary states can be beneficial in constructing entangling two-qubit operations. We investigate the general case of two multistate quantum systems coupled via a quantum resonator. The approach is illustrated with the examples of three systems: self-assembled InAs/GaAs quantum dots, NV centers in diamond, and superconducting transmon qubits. Fidelities of the gate operations are calculated based on numerical simulations of each system.

Curl-free vector potential observation on the macro-scale and a new dimension to the Lorentz trajectory

The recently reported curl-free vector potential observation on the macro-scale, which has been attributed to a macro-scale matter wave associated with the quantum modulation of the de Broglie wave along the magnetic field, is seen to be in apparent contravention with the Lorentz equation of classical electrodynamics, which as a descriptor on the macro-scale takes no cognizance of a curl-free vector potential. The two different formalisms—a deterministic one à la Lorentz and a probabilistic one by the quantum modulation—both existing on the macro-scale and, though in apparent contravention, complement each other and are essential for a complete description of all phenomena relating to charged particle dynamics. The quantum modulations which arise in consequence of transition across Landau levels appear as ‘hole’ auto-excitations in the Lorentz trajectory involving internal inelastic scattering. This lends a new dimension to the Lorentz trajectory which, though on the classical macro-scale, acts like a ‘quantum resonator’ and can now exist in a number of self-excited states labelled by the Landau level interval involved in the excitation, and which are of quantum origin and on the macro-scale, with the quantum modulations being the excitations.

Cumulative quantum mechanics (CQM) Part II. Application of cumulative quantum mechanics in describing the Vysikaylo polarization quantum-size effects

The processes of physical doping of nanostructured (meta-) materials have been investigated. Two types of interference and diffraction (in the center) in hollow quantum resonators for the de Broglie waves of electrons and two types of the Vysikaylo quantum-size effects due to the polarization capture of electrons in the cavity of quantum resonators are described on the basis of the cumulative quantum mechanics (CQM) formulated by the author. The first type of interference and, accordingly, diffraction in the resonator center corresponds to de Broglie-Fresnel interference (sin-wave with a node in the resonator center). This type is used to describe the localization (cumulation) of electrons in the atom quantum resonator with an atomic nucleus in the center. The second type of interference and, accordingly, diffraction is called Vysikaylo-de Broglie-Fraunhofer interference (diffraction with the antinode of the electron de Broglie wave in the center of a hollow resonator), wherein the Ψ n -functions of the electron infinitely cumulate (are focused by a polarization “mirror”) towards the center of a hollow quantum spherically or cylindrically symmetric resonator (Ψ n (r) ∼ cos(k n r)/r k ). It is shown that the cos-solutions, irregular in the resonator center, are regularized for any wave phenomena by the geometric coefficient. It is proved in the framework of CQM that, alongside with the classical energy spectrum for asymmetric Ψ n -functions (sin waves (overtones)) with E n ∼ n 2, for hollow quantum resonators, there exist and are realized in experiments the quantum resonances for symmetric Ψ n -functions (cos waves (the principal tone)) with E n ∼ (n − 1/2)2. The spectrum of energy states, localized by a barrier, with E n > 0 (a metastable IQ-particle (a partially open quantum dot, line, or well)), as in the case of E n < 0 (a stable FQ-particle (a close dot, line, or well)), is determined by the effective internal sizes of the box (R + r ind) with polarization forces effectively acting at the distance of r ind from the molecule. The comparison of the analytical results with the experimental observations proves convincingly the validity of the CQM application in describing the quantum-size effects in the case of physical doping of metamaterials. It has been demonstrated for the first time that, in nanocomposite materials, the pair of “eigenfunction Ψ n —self-energy E n” comprising the quantum state in the nanoworld noted by the basic quantum number n and in the mesoworld of nanocomposites by physically doped by traps is replaced by two nanoworld parameters: the nanocrystal diameter D and the relative resonance concentration of the modifier (a trap, such as C60, 70) ζn. The self-assembly of hollow allotropic forms of carbon on resonant electrons is discussed.

Cumulative quantum mechanics (CQM). Part I: Prerequisites and fundamentals of CQM

There is proposed a formulation of the fundamentals of cumulative quantum mechanics (CQM) that allows one to describe the resonance cos-waves with the ψ n function of an electron (ψ n (r) ∼ cos(k n r)/r k ) unlimited (with k ≠ 0) in the resonator center in hollow quantum resonators with any type of symmetry (plane—k = 0, spherical—k = 1, and cylindrical—k = 0.5). Irregular in the center of a resonator, the cos solutions are regularized in the resonator center by the geometric normalization coefficient corresponding to the symmetry type and being χ(r) = 2 k π1/2 r k at k ≠ 0 (if k = 0, then χ = 1). The stratification of the probability of finding the particle in the quantum resonator volume is similarly determined by the energy of a particle or a full set of squares of the corresponding quantum numbers ((n − 1/2)2 for cos-waves and n 2 for sin-waves) for any type of the resonator symmetry. An analytical CQM model of the polarization resonance electron capture (dynamic localization due to the self-formation of a potential barrier cumulating this electron into a molecule) is proposed. When there occurs the polarization capture of an electron by the allotropic hollow forms of carbon (fullerenes and nanotubes), the electron energy E n > 0. The problem on the Vysikaylo polarization effect of the first type (or the problem on polarization cumulation of the de Broglie waves of electrons with characteristic dimension of ∼ 1 nm) is reduced to the problem of G.A. Gamov: “a quantum particle in a box with a potential barrier on its boundary.” The energy spectrum of states localized by the barrier, E n > 0 (a metastable IQ particle is a partially open quantum dot, line, or pit), as in the case of E n < 0 (a stable FQ particle is a closed quantum dot, line, or pit) is determined by the effective internal dimensions of a box (R + r ind) with the polarization forces effectively acting at a distance r ind from the polarizable molecule. The CQM allows one to describe with E n > 0 both the limited cumulation of ψn(r)-functions for de Broglie-Fresnel generalized interference and the unlimited cumulation of ψn(r)-functions to the center of a quantum resonator with Vysikaylo-de Broglie-Fraunhofer generalized interference in hollow polarizable spherically or cylindrically symmetric quantum resonators for de Broglie electron waves. In the framework of the CQM, there have been analytically calculated the eigen quantum pairs: ψ n (r)-functions, respectively stratified profiles of the probability of a particle’s location in the resonator cavity, W n (r) and E n > 0, the eigen energies of the electrons localized in the quantum resonator (C60 and C70, etc.) by polarization forces. It is proved that, alongside with the classical energy spectrum for asymmetric ψ n -functions (sin-waves) with E n ∼ n 2 for hollow quantum resonators, there exist quantum resonances for symmetric ψ n -functions (cos-waves) with E n ∼ (n − 1/2)2, which can be realized in the experiments.

Full counting statistics of energy fluctuations in a driven quantum resonator

We consider the statistics of time-integrated energy fluctuations of a driven bosonic resonator (as measured by a QND detector), using the standard Keldysh prescription to define higher moments. We find that due to an effective cascading of fluctuations, these statistics are surprisingly non-classical: the low-temperature, quantum probability distribution is not equivalent to the high-temperature classical distribution evaluated at some effective temperature. Moreover, for a sufficiently large drive detuning and low temperatures, the Keldysh-ordered quasi-probability distribution characterizing these fluctuations fails to be positive-definite; this is similar to the full counting statistics of charge in superconducting systems. We argue that this indicates a kind of non-classical behaviour akin to that tested by Leggett-Garg inequalities.

A negative feedback controlled hybrid mode locked Nd : YAG laser using a semiconductor quantum dot saturable absorber

The parameters of a solid-state PbS quantum dot saturable absorber, optical elements, resonator and feedback circuit have been adjusted for stable and highly efficient hybrid mode-locking Nd : YAG laser operation. A highly stable microsecond pulse train (40–50 μs) containing about 5000 ps pulses and 3 mJ total train energy was generated with a repetition rate of 10 Hz. This all solid-state hybrid mode-locked Nd : YAG laser was used for synchronous pumping of a femtosecond Ti : sapphire laser.